If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is :

Options

A. 40
B. 44
C. 80
D. 88

Answer

To solve the problem, we need to find the product of two numbers \( A \) and \( B \) given the following conditions:

1. The sum of the two numbers is \( A + B = 22 \).
2. The sum of their squares is \( A^2 + B^2 = 404 \).

We can use these equations to find the product \( AB \).

### Step 1: Use the identity for the sum of squares
We know that:
\[ A^2 + B^2 = (A + B)^2 - 2AB \]
Substituting the known values into this equation:
\[ 404 = (22)^2 - 2AB \]

### Step 2: Calculate \( (A + B)^2 \)
Calculate \( (A + B)^2 \):
\[ (22)^2 = 484 \]

### Step 3: Substitute and rearrange the equation
Now substitute this value back into the equation:
\[ 404 = 484 - 2AB \]
Rearranging gives:
\[ 2AB = 484 - 404 \]
\[ 2AB = 80 \]

### Step 4: Solve for \( AB \)
Now divide both sides by 2:
\[ AB = \frac{80}{2} = 40 \]

### Conclusion
The product of the two numbers \( A \) and \( B \) is:
\[ \boxed{40} \]